A160233 -id:A160233 - cp's OEIS frontend

A212183 Largest odd divisor of A002183(n) (number of divisors of n-th highly composite number).

1, 1, 3, 1, 3, 1, 9, 5, 3, 1, 9, 5, 3, 15, 1, 9, 5, 3, 15, 1, 9, 5, 21, 45, 3, 25, 27, 15, 1, 9, 5, 21, 45, 3, 25, 27, 7, 15, 1, 9, 5, 21, 45, 3, 25, 27, 7, 15, 63, 1, 9, 75, 5, 21, 45, 3, 25, 27, 7, 15, 63, 1, 9, 75, 5, 21, 45, 3, 25, 105, 27, 7, 15, 63, 1, 9

Offset: 1

Matthew Vandermast, Jun 08 2012

nonn

The "odd part" (largest odd divisor) of the number of divisors of n is a function of the exponents >=2 in the prime factorization of n (cf. A212172, A212181).

The number 1 appears a total of 18 times (see Graeme link for proof). Ramanujan proved that no number appears an infinite number of times (see Ramanujan link). It would be interesting to know more about a) which odd numbers appear in the sequence and b) how many times a number of a given size can appear in the sequence. See also A160233.

			The highly composite number 48 has a total of 10 divisors. Since 48 = A002182(8), A002183(8) = 10. Since the largest odd divisor of 10 is 5, a(8) = 5.

Amiram Eldar, Table of n, a(n) for n = 1..10000
A. Flammenkamp, List of the first 1200 highly composite numbers
Graeme McRae, Highly Composite Numbers
S. Ramanujan, Highly Composite Numbers (p. 34).
S. Ramanujan, Highly composite numbers, Proc. Lond. Math. Soc. 14 (1915), 347-409; reprinted in Collected Papers, Ed. G. H. Hardy et al., Cambridge 1927; Chelsea, NY, 1962.

Cf. A000265, A002182, A002183, A212181.

A160233 gives the n-th integer that is the largest member of A002183 with its particular odd part.

a(n) = A000265(A002183(n)) = A212181(A002182(n)).

cp's OEIS Frontend

A212183 Largest odd divisor of A002183(n) (number of divisors of n-th highly composite number).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula